MEDT analysis of mechanism and selectivities in non-catalyzed and lewis acid-catalyzed diels–alder reactions between R-carvone and isoprene

Within the context of Molecular Electronic Density Theory (MEDT), this study investigates the Diels–Alder reaction among isoprene (2) and R-carvone (1R) applying DFT simulations, with and without Lewis acid (LA) catalysis. The results show that carvone (1R) acts as an electrophile and isoprene (2) as a nucleophile in a polar process. LA catalysis increases the electrophilicity of carvone, thereby improving the reactivity and selectivity of the reaction by reducing the activation Gibbs free energy. Parr functions reveal that the C5=C6 double bond is more reactive than the C9=C10 double bond, indicating chemoselectivity. The examination of the Electron Localization Function (ELF) reveals high regio- and stereoselectivity, indicating an asynchronous mechanism for the LA-catalyzed DA reaction. Furthermore, it is suggested that cycloadduct 3 has great anti-HIV potential because it exhibits lower binding energies than azidothymidine (AZT) in the docking studies of cycloadducts 3 and 4 amongst a primary HIV-1protein (1A8O plus 5W4Q).


Computational details
DFT calculations were performed by using the B3LYP functional 17,18 together with the 6-311++ G(d, p) basis set, employing the Gaussian 16 software package 19 .Theoretical reactivity indices 20,21 , were obtained by using the equations outlined in reference 21.Within the DFT framework various reactivity indices, encompassing the electronic chemical potential μ, chemical hardness η, global electrophilicity ω 22 , and nucleophilicity N 23,24 were evaluated at the B3LYP/6-31G(d) level.These indices were estimated based on the energies of the frontier molecular orbitals HOMO and LUMO, denoted as H and L, through the following expressions: µ . The empirical nucleophilicity N index can be expressed using the formula N = E HOMO (Nu) − E HOMO (TCE), where TCE represents tetracyanoethylene 23 .To determine the electrophilic P + k and nucleophilic P − k Parr functions 25 , the atomic spin densities (ASD) of the radical anion and the radial cation of the reactants were analyzed.
The ELF 16 was computed using the Multiwfn software 26 .Additionally, a natural bond orbital (NBO) analysis 27 was conducted to provide further insights into the results.
The global electron density transfer (GEDT) 28 was calculated by summing the natural atomic charges (q) for the atoms in the transition state structures (TSs) of each framework, as determined by a natural population analysis (NPA) 29,30 .
The intrinsic reaction coordinate (IRC) was used to examine the transition state (TS) associated with the corresponding minimum on the potential energy surfaces 31,32 .

Ethics approval
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Consent to participate
The manuscript is approved by all authors for publication.

Results and discussion
The present MEDT 15 study is organized into six specific sections: (1) the initial section encompasses an ELF topological analysis of the electronic structure of the reactants; (2) in the second section the theoretical reactivity indices for the reactants are examined; (3) the third section is dedicated to investigating competitive reaction paths associated with the non-catalyzed and LA-catalyzed DA reactions outlined in Scheme 1; (4) the fourth section introduces a Bond Evolution Theory 33 (BET) study, which focuses on the more favorable reaction path in the DA reaction between carvone 1R and isoprene 2, both in the presence and absence of the LA catalyst; (5)  in the fifth section, an analysis of ELF compares the preferred DA reaction between carvone 1R and isoprene www.nature.com/scientificreports/ELF topological analysis of the electronic structures of carvone 1R, LA:carvone complex 1R:LA, and isoprene 2 Figure 1 provides information on the ELF valence attractor locations, ELF localization domains, and population results for carvone 1R, LA:carvone complex 1R:EtAlCl 2 (1R:Al), and isoprene 2. ELF topological analysis of isoprene 2 in Fig. 1, shows the presence of six disynaptic basins.Notably, the C1-C2 and C3-C4 bonding regions exhibit two pairs of V(Cx,Cy) disynaptic basins with a total population of 3.39 e and 3.42 e, respectively, which correspond to two depopulated C-C double bonds, and a V(C2,C3) disynaptic basin integrating 2.18 e, corresponding to a C-C single bond.
Coordination of the EtAlCl 2 LA catalyst to the O8 oxygen of carvone 1R slightly modifies the C=C-C=O framework of the LA:carvone complex 1R:LA.Thus, the electron density population of the conjugated C5-C6 double bond decreases from 3.40 to 3.27 e, while that of the C9-C10 double bond remains relatively constant with a total electron density population of 3.49 e.

Analysis of the reactivity indices at the GS of the reagents
Numerous studies devoted to DA reactions have shown that the analysis of the reactivity indices is a powerful tool to predict and understand the reactivity in polar and ionic organic reactions 34 .
The electrophilicity ω 22 , and nucleophilicity N 23,24 indices of carvone 1R are 1.41 eV and 2.67 eV, respectively, being classified as a moderate electrophile and a moderate nucleophile within the corresponding scales 23 .Coordination of the EtAlCl 2 Lewis acid to the O8 oxygen of carvone 1R notably increases the electrophilicity ω index of the LA:carvone complex 1R:Al, ω = 3.25 eV, and slightly decreases it nucleophilicity N index to 2.42 eV.Thus, LA:carvone complex 1R:Al, with a ω > 3.00 eV, is classified as a superelectrophile 36 .On the other hand, the electrophilicity ω and nucleophilicity N indices of isoprene 2 are 0.90 eV and 2.94 eV, respectively, being classified as a moderate electrophile and in the borderline of strong nucleophile within the corresponding scales.
Consequently, it is expected that while the polar DA reaction between carvone 1R and isoprene 2 will have some polar character, that involving LA:carvone complex 1R:Al will have high polar character, showing a high acceleration 37 .
Recent studies on polar cycloaddition reactions have generally shown that the preferred regioselective pathways often involve a two-center interaction between the most electrophilic site of one reactant and the most nucleophilic site of the other 38 .As indicated in previous studies, the analysis of the electrophilic P + k and nucleophilic P − k Parr functions 25 , arising from the surplus spin electron density transferred via the GEDT 28 mechanism from the nucleophile to the electrophile, have proven to be the most precise and illuminating tools for evaluating local reactivity in polar and ionic reactions.
Figure 2 illustrates that the carbon atom C4 of isoprene 2 corresponds with the highest nucleophilic center ( P − C4 = 0.56) of this species, while the electrophilic P + k Parr functions for carvone 1R and the LA:carvone complex 1R:Al indicate that C5 exhibits the highest electrophilic center ( P + k = 0.53 ).Hence, in agreement with experimental findings, the preferred electrophile-nucleophile interaction in these polar DA reactions occurs along the two-center interactions involving carbon atom C4 of isoprene 2 and carbon atom C5 of carvone 1R and the LA: carvone complex 1R:Al.The electrophilic P + k Parr functions of the C9 and C10 carbons of 1R and 1R:Al ( P + k < 0 ) indicate that these two unsaturated carbons are electrophilically deactivated.Consequently, the corresponding polar DA reactions will be completely regio-and chemoselective.

Exploring the reactions paths associated with in the DA reactions of carvone 1R and LA:carvone complex 1R:Al with isoprene 2
Initially, potential energy surface of the reaction paths associated in the DA reactions of carvone 1R and LA:carvone complex 1R:Al with isoprene 2 were investigated.The polar DA reactions are endo stereoselective,  only the endo/exo stereoselectivity for the more favorable regioisomeric reaction paths were studied (see Schemes 2 and 3).These reaction paths involve the stereoselectivity arising from the asymmetry of carvone 1R and LA:carvone complex 1R:Al with isoprene 2, as well as the chemoselective attack of isoprene 2 on the double bonds C5-C6 of carvone 1R and LA:carvone complex 1R:Al.Moreover, these C-C double bonds are amenable to stereoselective attacks from either side.The experimental findings indicate that the LA catalyzed DA reaction of carvone 1R with isoprene 2 takes place with a complete selectivity, involving solely the C5-C6 double bond, and with a complete regioselectivity, resulting in the production of two stereoisomers associated with the formation of the C1-C6 and C4-C5 single bonds (see Scheme 1).To elucidate the observed regio-, and stereoselectivity, a comprehensive investigation of these six reaction pathways, both in the absence and the presence of the EtAlCl 2 LA catalyst was conducted.
Along each of the six reaction paths only one TS and one CA was characterized for both the non-catalyzed and LA catalyzed DA reactions between carvone 1R and isoprene 2 (see Schemes 2 and 3), indicating that these DA reactions take place via a one-step mechanism.Figure 3 illustrates the relative Gibbs free energy values for the stationary points associated to the non-catalyzed and LA catalyzed DA reactions of carvone 1R and isoprene 2 computed in toluene at 25 °C.For detailed thermodynamic data, frequency details, and Cartesian coordinates for the TSs are provided in Supplementary.
Analysis of Tables S1 and Tables S2 highlights the activation enthalpy of the 2 + 4 cycloaddition reaction between R-Carvone (1R) and Isoprene (2), with and without catalyst.The tables provide detailed comparisons of the activation enthalpies (∆H) for different systems.For the TSn-1-Al system, the activation enthalpy without catalyst is 29.27 kcal/mol, while with catalyst it is 19.53 kcal/mol, indicating a significant reduction of 9.74 kcal/ mol, suggesting significant catalytic efficiency.In contrast, for the TSx-1-Al system, the reduction is less marked, with the enthalpy of activation falling from 28.77 kcal/mol without catalyst to 27.35 kcal/mol with catalyst, a reduction of 1.42 kcal/mol.For the TSx-2-Al system, the reduction of 6.51 kcal/mol is notable, with activation enthalpy falling from 28.74 kcal/mol without catalyst to 22.23 kcal/mol with catalyst.The TSn-2-Al system shows little catalytic influence, with a reduction of 1.2 kcal/mol.The TSn-3-Al system shows a notable reduction of 7.12 kcal/mol, and finally, the TSx-3-Al system shows a significant reduction of 8.16 kcal/mol.In conclusion, the analysis reveals that the presence of a catalyst reduces the enthalpy of activation in all the systems studied, although the effect varies according to the specific system, with the TSn-1-Al, TSx-2-Al, TSn-3-Al, and TSx-3-Al systems showing notable reductions in enthalpy of activation.
The relationship ΔG = ΔH − TΔS shows that the free enthalpy of activation is influenced by entropy.Negative entropy values (ΔS) indicate that their contribution (TΔS) increases ΔG.Despite this increase, the reduction in ΔH, and therefore entropy ΔS, destabilizes the reaction.Figure 3 shows that the free energies of activation of the two stereoisomeric reaction pathways in the uncatalyzed reaction range from 42.72 to 43 Figure 3 shows a summary of the free energies data.These relative Gibbs free energies show that TSn-1-Al is kinetically more favored than TSn-1 by an average of 9.93 kcal/mol, however the thermodynamic stability of P-n-1-Al is estimated at 1.34 kcal/mol when compared to P-x-2-Al.These findings suggest that the regioisomer P-n-1-Al is obtained due to uncontrolled kinetic factors, while Experimental finding indicate that, P-n-1-Al is the predominant product, with a yield of 92.06%, while P-x-2-Al is obtained with only a yield of 7.94%.
Furthermore, TSx-1-Al (34.92 kcal/mol) is 8.88 lower compared to that of TSx-1 (43.80 kcal/mol), this observation indicates a remarkable enhancement in the efficiency of the reaction in the presence of the catalyst.
This trend is consistent across all transition states, highlighting the catalytic prowess of Et2AlCl3 in facilitating the Diels-Alder reaction between carvone 1R and isoprene 2.
The most favorable reaction path result in the formation of stereoisomer P-n-1-Al as the major product and stereoisomer P-x-2-Al as the minor product, occurring through TSn-1-Al and TSx-2-Al, respectively.These TSs are situated 33.70 kcal/mol (TSn-1-Al) and 34.92 kcal/mol (TSx-2-Al) kcal.mol-1above the reactants.The activation free energy difference between TSn-1-Al and TSx-2-Al, represented by ΔΔG = 1.22 kcal/mol, signifies significant regioselectivity observed experimentally in this LA-catalyzed 42DC reaction.
The optimized geometries in toluene of the TSs involved in the LA catalyzed DA reaction of LA: carvone complex 1R:Al with isoprene 2 are displayed in Fig. 4.
The GEDT values calculated at the more favorable TSs associated to the attach of isoprene 2 on the attached to the C5-C6 double bond of carvone 1R have a polar character, with GEDT values less than 0.20 e, while the TSs associated to the attach of isoprene 2 on the C5-C6 double bond of LA:carvone complex 1R-Al, which present a GEDT > 0.30 e, have a very high polar character as a consequence of the superelectrophilic character of the LA:carvone complex 1R-Al (see Table 1).The GEDT, which fluxes from isoprene 2 to LA:carvone complex 1R-Al permits to classify the experimental LA catalyzed DA reaction as the FEDT 35,36 .

BET study of the molecular mechanisms in the non-catalyzed and LA catalyzed DA reaction involving carvone 1R and isoprene 2
To understand the bonding changes occurring along the most favorable reaction path of the DA reaction involving carvone 1R and LA:carvone complex 1R:Al with isoprene 2, via TSn-1 and TSn-1-Al, respectively, a BET investigation was carried out 33 .This analysis focused on the redistribution of electron density along the selected reaction paths, as illustrated in Figs. 6 and 7. BET is an invaluable tool for elucidating alterations in bonding throughout a reaction path.It offers valuable insights into the nature of electronic changes associated with a particular chemical mechanism 39 .Detailed information about the two BET can be found in Tables S3 and Tables S4 in the Supporting Information.Figures 5 and 6     The two BET studies provide the following key findings: (1) the formation of the two C-C single bonds occurs in two distinct phases along the IRC, in the non-catalyzed and LA catalyzed DA reactions (2) in the absence of the LA catalyst, a new V(C4) monosynaptic basin, with an initial electron population of 0.19 e, is created at structure S6.The population of this monosynaptic basin increases at TSn-1.In contrast to the non-catalyzed DA reaction where the C4-C5 single bond is formed after to pass TSn-1, in the LA catalyzed reaction, the C-C single bond is formed before to reach TSn-1-Al; (3) in both non-catalyzed and LA catalyzed processes, the fusion of two pseudoradical centers 40 , characterized by the presence of the V(C4) and V(C5) monosynaptic basins, permit the formation of the first C4-C5 single bond at a distance of 1.88 Å in the non-catalyzed process, after to pass TSn-1, and a distance of 1.97 Å in the LA catalyzed one, at the TSn-1-Al 28 ; (4) in the early stages of the reaction, the C5-C6 double bond in carvone 1R experiences a gradual reduction in electron population, resulting in a decrease from 3.32e to 1.93e in the absence of the LA catalyst, and from 3.25e to 1.92e when the catalyst is present.These bonding changes are demanded for the subsequent formation of the C5 pseudoradical centers.A similar behavior is observed in the C1-C2 and C3-C4 double bonds of isoprene 2. In particular, in the noncatalyzed DA reaction, the electron population of the C1-C2 double bond decreases from 3.32e to 1.93e, while in the LA catalyzed reaction, it decreases from 3.25e to 1.92e.The electron population also decreases for the C3-C4 double bond, dropping from 3.32e to 1.93e in the non-catalyzed process and from 3.25e to 1.92e in the LA catalyzed reaction; (6) in the LA catalyzed reaction, at structure Sʹ22, two monosynaptic basins, V(C1) and V(C6), are simultaneously created, with an electron populations of 0.19 and 0.36 e, respectively (as illustrated in Fig. 6).These V(C1) and V(C6) monosynaptic basins correspond to pseudoradical centers located at C1 and C6 carbons, which are demanded for the subsequent creation of the second C1-C6 single bond.Subsequently, at structure Sʹ23, both V(C1) and V(C6) monosynaptic basins disappear, making way for the formation of a new disynaptic basin, V(C1,C6), with an initial population of 0.97e (as illustrated in Fig. 6).These changes in electron density indicate that the second C1-C6 single bond has been formed at a C-C distance of 2.08 Å by the coupling of the two C1 and C6 pseudoradical centers.In contrast, in the non-catalyzed process, at structure S17, a new disynaptic basin V(C1,C6) appears, with an initial electron population of 1.21e (as depicted in Fig. 5).These electronic changes signify the formation of the second single bond C1-C6 at a C-C distance of 2.07 Å through the fusion of the electron densities of the two V(C1) and V(C6) monosynaptic basins, which integrated 0.50 and 0.64e, respectively, at structure S12; (6) moving from structures Sʹ24 to Sʹ40 in the catalyst reaction, there is a relaxation process leading to the formation of the final CA 3.This progression aligns with the expected structure for the CA 3, as depicted in Sʹ40 in Fig. 6; (7) based on these behaviors, it can be concluded that the LA catalyzed DA reaction follows a high asynchronous, non-concerted molecular mechanism.This mechanism can be defined as a two-stage one-step process 41 , as the creation of the second C1-C6 single bond begins after that the formation of the first C4-C5 single bond has been established in 80%.

Molecular docking
The global population faces the problem of viral infections and the emergence of life-threatening diseases caused by various viruses, including HIV-1 42 .HIV-1, the virus accountable for AIDS (Acquired Immunodeficiency Syndrome), substantially undermines the immune system, leading to numerous health-related complications.
To address this critical issue, molecular docking studies have been conducted, offering the potential to save time, expedite early preclinical research, and significantly reduce costs.
This technique has the capability to become a powerful tool in the development of strategies to combat these diseases and build a robust arsenal against them.
This section details a docking study conducted to explore potential interactions between the examined compounds and the HIV-1 protein.The central aim of this investigation is to gain a more profound insight into how these compounds can bind to and interact with viral protein.Consequently, this allows for a comparative analysis with the Azidothymidine (AZT) target, offering valuable insights into the potential contributions of these compounds in the fields of HIV-1 research and therapy.Ultimately, this study enhances our comprehension of their effectiveness and the mechanisms they employ to combat the viral virus.
Molecular docking studies require that both the ligands (product 3, product 4, and Azidothymidine) and the HIV-1 target (PDB ID: 5W4Q and 1A8O) possess a three-dimensional structure.The three-dimensional structures for 5W4Q and 1A8O were downloaded from the RCSB Protein Data Bank 43,44 .However, for the AZT ligand, its three-dimensional structure was obtained from PubChem, a database that provides comprehensive information, encompassing both chemical data and chemical structures 45 .
Molecular docking simulations were conducted using Auto Dock Tools 1.5.6 46 .In order to determine the molecular binding affinity of the protein-ligand complex, to visualize intricate interactions and elucidate the 2D and 3D structures of the ligand compounds docked with the HIV-1 protease protein (PDB ID: 5W4Q and 1A8O), BIOVIA Discovery Studio Visualizer and PyMol the bioinformatics software were employed 47,48 .Before the compounds were docked with the HIV-1 target, the proteins were preprocessed by eliminating water molecules and incorporating polar hydrogens and Kollman charges using ADT.
Based on the results of the docking studies, the data for two ligands with the HIV-1 protease, as well as a comparison to Azidothymidine as an antiviral drug, are indeed provided in Table 2.
The interactions between the ligands and the macromolecular target (Contrast with AZT) were predicted in both 2D and 3D using BIOVIA Discovery Studio Visualizer, these predictions are presented in Figs.7 and 8.
According to the data provided in Table 3, the binding energy for the two ligand compounds and the drug AZT with the HIV-1 protein receptor falls within the range of − 5.4 kcal/mol to − 5.7 kcal/mol for 5W4Q and − 5.5 kcal/mol to − 5.7 kcal/mol for 1A8O.
Figure 7 illustrates that ligand 1 and 2 engage in Pi-alkyl and alkyl interactions with amino acid residues ALA174, PRO34, PRO147, TYR145, and ALA31 within the VIH-1 (5W4Q) protein complex.On the other hand, Fig. 8 shows an alkyl interaction with amino acid residues LYZ158, CYS198, CYS218, and ILE201 within the protein 1A8O complex.
In Fig. 8, a carbon-hydrogen bond is observed with amino acid residue ASN195 in the ligand 1 when docked with the 1A8O protein, at a distance of 2.07 Å.Likewise, within the ligand 2 complex interacting with protein 1A8O, a carbon-hydrogen bond is detected with the amino acid residue ASN195, occurring at a distance of 2.04 Å.
In interaction analysis between AZT and the VIH-1 main protease 5W4Q, it is observed that OH and O form conventional hydrogen bond interactions with the ASN-139 and LYS-182 residues, respectively.Additionally, there are p-alkyl interactions with the ILE-37, PRO-34, and ARG-173 residues, as revealed by the docking results.
Conversely, in the case of protein 1A8O, conventional hydrogen bond interactions are detected at amino acid residues LYS158, PRO-157, PHE-161, GLN-155.Furthermore, there is a Pi-Sulfur interaction with CYS-218 and CYS198, as well as attractive charge interactions with amino acid GLY-220, according to the docking analysis.
Based on the visualized interactions of the ligands (P3) and (P4) with 5W4Q, we observe a significant interaction for the inhibition of HIV-1 compared to AZT, furthermore, the binding affinity infers that [5W4Q-ligandP3] and [5W4Q-ligandP4] exhibit − 5.7 kcal/mol and − 5.6 kcal/mol, respectively, representing less affinity among www.nature.com/scientificreports/ the studied ligands.These findings suggest their potential as drug candidates against the HIV-1 5W4Q protein (Table 3).

Conclusion
The EtAlCl 2 LA catalyzed DA reaction of carvone 1R and isoprene 2, has been studied within MEDT.The chemo-, regio-, and diastereoselectivity aspects of this LA catalyzed DA reaction have been analyzed by performing DFT calculations at B3LYP/6-311++ G(d, p) computational level.This DA reaction proceeds through

Figure 1 .
Figure 1.Displays the ELF localization domains of isoprene 2, carvone 1R and LA: carvone complex 1R:LA using the B3LYP/6-311++ G (d,p) method.These domains are revealed with an ELF isosurface value of 0.75, and the populations (red values) and natural atomic charges (green value) for each compound are shown in (e).

Figure 2 .
Figure 2. 3D representations of the Mulliken atomic spin densities of the radical anion of carvone 1R and LA:carvone complex 1R:Al, and those of the radical cation of isoprene 2, together with the electrophilic P + k Parr functions of 1R and LA:carvone complex 1R:Al and the nucleophilic P − k Parr functions of with isoprene 2.

Figure 3 .
Figure 3. Depicts ΔG of DA reaction between carvone 1R and isoprene 2 in the presence of toluene at 25 °C, under both non-catalyzed and EtAlCl 2 -catalyzed conditions.
illustrate the positions of ELF basin attractors for the most relevant structures SX involved in the formation of the new C1-C6 and C4-C5 single bonds, in both noncatalyzed and LA catalyzed processes.

Figure 4 .
Figure 4.The optimized geometries in toluene of the TSs for the LA catalyzed DA reaction between carvone 1R:Al and isoprene 2. Non-catalyzed values are presented in blue, and distances are given in angstroms (Å).

Figure 5 .
Figure 5. ELF attractors at critical points along the IRC, illustrating the formation of C4-C5 and C1-C6 single bonds in the non-catalyzed DA reaction between carvone 1R and isoprene 2.

Figure 6 .
Figure 6.ELF attractors at critical points along the IRC, illustrating the formation of C4-C5 and C1-C6 single bonds in the LA catalyzed DA reaction between carvone 1R and isoprene 2.

Figure 8 . 3 .
Figure 8. Binding orientation and molecular interactions of the the CA3, CA4 and Azidothymidine compounds into the active sites of 1A8O.

2 ,
considering both the presence and absence of an EtAlCl 2 LA catalyst; finally, (6) the sixth section explores molecular docking experiments that investigate the activities of the CAs against the main proteases associated with HIV-1 infection, namely, 5W4Q and 1A8O.

Scheme 3 .
Competitive reaction pathways for were calculated at a temperature of 25 °C, in the presence of toluene and a pressure of 1 atm the LA catalyzed DA reactions of LA: carvone complex 1R:Al with isoprene 2 (the energies are in kcal/mol) (The value in blue are the free energies, while green value are enthalpies).

Table 2 .
GEDT values for non-catalyzed and LA catalyzed DA reactions, measured in electron units.Significant values are in bold.